LMFDB - Embedded newform 1792.2.m.f.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			449.2
Root			$-0.709944 + 0.925217i$ of defining polynomial
Character	$\chi$	$=$	1792.449
Dual form			1792.2.m.f.1345.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.04137 + 2.04137i) q^{3} +(-0.701647 - 0.701647i) q^{5} -1.00000i q^{7} -5.33435i q^{9} +O(q^{10})$	\(q+(-2.04137 + 2.04137i) q^{3} +(-0.701647 - 0.701647i) q^{5} -1.00000i q^{7} -5.33435i q^{9} +(2.41989 + 2.41989i) q^{11} +(-1.96098 + 1.96098i) q^{13} +2.86464 q^{15} -6.93050 q^{17} +(-1.38948 + 1.38948i) q^{19} +(2.04137 + 2.04137i) q^{21} -2.05612i q^{23} -4.01538i q^{25} +(4.76526 + 4.76526i) q^{27} +(5.34414 - 5.34414i) q^{29} +5.23708 q^{31} -9.87975 q^{33} +(-0.701647 + 0.701647i) q^{35} +(-6.58401 - 6.58401i) q^{37} -8.00617i q^{39} -0.949797i q^{41} +(5.95343 + 5.95343i) q^{43} +(-3.74283 + 3.74283i) q^{45} +4.64785 q^{47} -1.00000 q^{49} +(14.1477 - 14.1477i) q^{51} +(7.24791 + 7.24791i) q^{53} -3.39582i q^{55} -5.67289i q^{57} +(-8.58048 - 8.58048i) q^{59} +(2.81502 - 2.81502i) q^{61} -5.33435 q^{63} +2.75184 q^{65} +(-9.07198 + 9.07198i) q^{67} +(4.19729 + 4.19729i) q^{69} -3.60510i q^{71} -6.53179i q^{73} +(8.19686 + 8.19686i) q^{75} +(2.41989 - 2.41989i) q^{77} +13.7819 q^{79} -3.45223 q^{81} +(4.49372 - 4.49372i) q^{83} +(4.86277 + 4.86277i) q^{85} +21.8187i q^{87} -0.428825i q^{89} +(1.96098 + 1.96098i) q^{91} +(-10.6908 + 10.6908i) q^{93} +1.94986 q^{95} +14.6339 q^{97} +(12.9085 - 12.9085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 4 q^{5}+O(q^{10}) $ 16 * q - 4 * q^3 + 4 * q^5	$ 16 q - 4 q^{3} + 4 q^{5} + 8 q^{11} - 12 q^{13} - 8 q^{17} - 4 q^{19} + 4 q^{21} + 56 q^{27} + 8 q^{31} + 16 q^{33} + 4 q^{35} + 8 q^{37} + 24 q^{43} + 36 q^{45} + 40 q^{47} - 16 q^{49} - 24 q^{51} + 32 q^{53} + 4 q^{59} + 20 q^{61} - 24 q^{63} + 72 q^{65} - 32 q^{67} - 56 q^{69} + 28 q^{75} + 8 q^{77} - 40 q^{81} - 36 q^{83} + 12 q^{91} - 8 q^{93} + 80 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 + 4 * q^5 + 8 * q^11 - 12 * q^13 - 8 * q^17 - 4 * q^19 + 4 * q^21 + 56 * q^27 + 8 * q^31 + 16 * q^33 + 4 * q^35 + 8 * q^37 + 24 * q^43 + 36 * q^45 + 40 * q^47 - 16 * q^49 - 24 * q^51 + 32 * q^53 + 4 * q^59 + 20 * q^61 - 24 * q^63 + 72 * q^65 - 32 * q^67 - 56 * q^69 + 28 * q^75 + 8 * q^77 - 40 * q^81 - 36 * q^83 + 12 * q^91 - 8 * q^93 + 80 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.04137	+	2.04137i	−1.17858	+	1.17858i	−0.198478	+	0.980105i	$0.563600\pi$
$3$	−2.04137	+	2.04137i	−1.17858	+	1.17858i	−0.980105	+	0.198478i	$0.936400\pi$
$4$		0			0
$5$	−0.701647	−	0.701647i	−0.313786	−	0.313786i	0.532588	−	0.846375i	$-0.321219\pi$
$5$	−0.701647	−	0.701647i	−0.313786	−	0.313786i	−0.846375	+	0.532588i	$0.821219\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	5.33435i		−	1.77812i
$10$		0			0
$11$	2.41989	+	2.41989i	0.729624	+	0.729624i	0.970545	−	0.240921i	$-0.0774495\pi$
$11$	2.41989	+	2.41989i	0.729624	+	0.729624i	−0.240921	+	0.970545i	$0.577449\pi$
$12$		0			0
$13$	−1.96098	+	1.96098i	−0.543879	+	0.543879i	−0.924664	−	0.380784i	$-0.875654\pi$
$13$	−1.96098	+	1.96098i	−0.543879	+	0.543879i	0.380784	+	0.924664i	$0.375654\pi$
$14$		0			0
$15$	2.86464			0.739646
$16$		0			0
$17$	−6.93050			−1.68089			−0.840447	−	0.541894i	$-0.817707\pi$
$17$	−6.93050			−1.68089			−0.840447	+	0.541894i	$0.817707\pi$
$18$		0			0
$19$	−1.38948	+	1.38948i	−0.318770	+	0.318770i	−0.848294	−	0.529525i	$-0.822370\pi$
$19$	−1.38948	+	1.38948i	−0.318770	+	0.318770i	0.529525	+	0.848294i	$0.322370\pi$
$20$		0			0
$21$	2.04137	+	2.04137i	0.445463	+	0.445463i
$22$		0			0
$23$		−	2.05612i		−	0.428730i	−0.976754	−	0.214365i	$-0.931232\pi$
$23$		−	2.05612i		−	0.428730i	0.976754	−	0.214365i	$-0.0687682\pi$
$24$		0			0
$25$		−	4.01538i		−	0.803076i
$26$		0			0
$27$	4.76526	+	4.76526i	0.917074	+	0.917074i
$28$		0			0
$29$	5.34414	−	5.34414i	0.992381	−	0.992381i	−0.00758978	−	0.999971i	$-0.502416\pi$
$29$	5.34414	−	5.34414i	0.992381	−	0.992381i	0.999971	+	0.00758978i	$0.00241593\pi$
$30$		0			0
$31$	5.23708			0.940607			0.470304	−	0.882505i	$-0.344144\pi$
$31$	5.23708			0.940607			0.470304	+	0.882505i	$0.344144\pi$
$32$		0			0
$33$	−9.87975			−1.71984
$34$		0			0
$35$	−0.701647	+	0.701647i	−0.118600	+	0.118600i
$36$		0			0
$37$	−6.58401	−	6.58401i	−1.08240	−	1.08240i	−0.996285	−	0.0861191i	$-0.972553\pi$
$37$	−6.58401	−	6.58401i	−1.08240	−	1.08240i	−0.0861191	−	0.996285i	$-0.527447\pi$
$38$		0			0
$39$		−	8.00617i		−	1.28201i
$40$		0			0
$41$		−	0.949797i		−	0.148333i	−0.997246	−	0.0741667i	$-0.976370\pi$
$41$		−	0.949797i		−	0.148333i	0.997246	−	0.0741667i	$-0.0236297\pi$
$42$		0			0
$43$	5.95343	+	5.95343i	0.907889	+	0.907889i	0.996102	−	0.0882122i	$-0.0281154\pi$
$43$	5.95343	+	5.95343i	0.907889	+	0.907889i	−0.0882122	+	0.996102i	$0.528115\pi$
$44$		0			0
$45$	−3.74283	+	3.74283i	−0.557948	+	0.557948i
$46$		0			0
$47$	4.64785			0.677959			0.338980	−	0.940794i	$-0.389918\pi$
$47$	4.64785			0.677959			0.338980	+	0.940794i	$0.389918\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	14.1477	−	14.1477i	1.98107	−	1.98107i
$52$		0			0
$53$	7.24791	+	7.24791i	0.995577	+	0.995577i	0.999990	−	0.00441361i	$-0.00140490\pi$
$53$	7.24791	+	7.24791i	0.995577	+	0.995577i	−0.00441361	+	0.999990i	$0.501405\pi$
$54$		0			0
$55$		−	3.39582i		−	0.457892i
$56$		0			0
$57$		−	5.67289i		−	0.751393i
$58$		0			0
$59$	−8.58048	−	8.58048i	−1.11708	−	1.11708i	−0.992167	−	0.124916i	$-0.960134\pi$
$59$	−8.58048	−	8.58048i	−1.11708	−	1.11708i	−0.124916	−	0.992167i	$-0.539866\pi$
$60$		0			0
$61$	2.81502	−	2.81502i	0.360427	−	0.360427i	−0.503543	−	0.863970i	$-0.667970\pi$
$61$	2.81502	−	2.81502i	0.360427	−	0.360427i	0.863970	+	0.503543i	$0.167970\pi$
$62$		0			0
$63$	−5.33435			−0.672065
$64$		0			0
$65$	2.75184			0.341324
$66$		0			0
$67$	−9.07198	+	9.07198i	−1.10832	+	1.10832i	−0.114947	+	0.993372i	$0.536670\pi$
$67$	−9.07198	+	9.07198i	−1.10832	+	1.10832i	−0.993372	+	0.114947i	$0.963330\pi$
$68$		0			0
$69$	4.19729	+	4.19729i	0.505294	+	0.505294i
$70$		0			0
$71$		−	3.60510i		−	0.427847i	−0.976850	−	0.213923i	$-0.931376\pi$
$71$		−	3.60510i		−	0.427847i	0.976850	−	0.213923i	$-0.0686243\pi$
$72$		0			0
$73$		−	6.53179i		−	0.764488i	−0.924061	−	0.382244i	$-0.875151\pi$
$73$		−	6.53179i		−	0.764488i	0.924061	−	0.382244i	$-0.124849\pi$
$74$		0			0
$75$	8.19686	+	8.19686i	0.946492	+	0.946492i
$76$		0			0
$77$	2.41989	−	2.41989i	0.275772	−	0.275772i
$78$		0			0
$79$	13.7819			1.55059			0.775293	−	0.631602i	$-0.217602\pi$
$79$	13.7819			1.55059			0.775293	+	0.631602i	$0.217602\pi$
$80$		0			0
$81$	−3.45223			−0.383581
$82$		0			0
$83$	4.49372	−	4.49372i	0.493250	−	0.493250i	−0.416079	−	0.909329i	$-0.636596\pi$
$83$	4.49372	−	4.49372i	0.493250	−	0.493250i	0.909329	+	0.416079i	$0.136596\pi$
$84$		0			0
$85$	4.86277	+	4.86277i	0.527441	+	0.527441i
$86$		0			0
$87$			21.8187i			2.33921i
$88$		0			0
$89$		−	0.428825i		−	0.0454554i	−0.999742	−	0.0227277i	$-0.992765\pi$
$89$		−	0.428825i		−	0.0454554i	0.999742	−	0.0227277i	$-0.00723508\pi$
$90$		0			0
$91$	1.96098	+	1.96098i	0.205567	+	0.205567i
$92$		0			0
$93$	−10.6908	+	10.6908i	−1.10858	+	1.10858i
$94$		0			0
$95$	1.94986			0.200051
$96$		0			0
$97$	14.6339			1.48584			0.742922	−	0.669378i	$-0.233439\pi$
$97$	14.6339			1.48584			0.742922	+	0.669378i	$0.233439\pi$
$98$		0			0
$99$	12.9085	−	12.9085i	1.29736	−	1.29736i
$100$		0			0
$101$	11.2007	+	11.2007i	1.11451	+	1.11451i	0.992533	+	0.121978i	$0.0389237\pi$
$101$	11.2007	+	11.2007i	1.11451	+	1.11451i	0.121978	+	0.992533i	$0.461076\pi$
$102$		0			0
$103$			18.4673i			1.81964i	0.415005	+	0.909819i	$0.363780\pi$
$103$			18.4673i			1.81964i	−0.415005	+	0.909819i	$0.636220\pi$
$104$		0			0
$105$		−	2.86464i		−	0.279560i
$106$		0			0
$107$	0.146171	+	0.146171i	0.0141309	+	0.0141309i	0.714137	−	0.700006i	$-0.246819\pi$
$107$	0.146171	+	0.146171i	0.0141309	+	0.0141309i	−0.700006	+	0.714137i	$0.746819\pi$
$108$		0			0
$109$	−0.309414	+	0.309414i	−0.0296365	+	0.0296365i	−0.721770	−	0.692133i	$-0.756671\pi$
$109$	−0.309414	+	0.309414i	−0.0296365	+	0.0296365i	0.692133	+	0.721770i	$0.256671\pi$
$110$		0			0
$111$	26.8807			2.55141
$112$		0			0
$113$	16.7193			1.57282			0.786409	−	0.617706i	$-0.211938\pi$
$113$	16.7193			1.57282			0.786409	+	0.617706i	$0.211938\pi$
$114$		0			0
$115$	−1.44267	+	1.44267i	−0.134530	+	0.134530i
$116$		0			0
$117$	10.4606	+	10.4606i	0.967081	+	0.967081i
$118$		0			0
$119$			6.93050i			0.635318i
$120$		0			0
$121$			0.711717i			0.0647016i
$122$		0			0
$123$	1.93888	+	1.93888i	0.174823	+	0.174823i
$124$		0			0
$125$	−6.32562	+	6.32562i	−0.565781	+	0.565781i
$126$		0			0
$127$	−4.91639			−0.436259			−0.218130	−	0.975920i	$-0.569996\pi$
$127$	−4.91639			−0.436259			−0.218130	+	0.975920i	$0.569996\pi$
$128$		0			0
$129$	−24.3063			−2.14005
$130$		0			0
$131$	−1.10403	+	1.10403i	−0.0964592	+	0.0964592i	−0.753690	−	0.657230i	$-0.771728\pi$
$131$	−1.10403	+	1.10403i	−0.0964592	+	0.0964592i	0.657230	+	0.753690i	$0.271728\pi$
$132$		0			0
$133$	1.38948	+	1.38948i	0.120484	+	0.120484i
$134$		0			0
$135$		−	6.68706i		−	0.575531i
$136$		0			0
$137$			0.184924i			0.0157991i	0.999969	+	0.00789957i	$0.00251454\pi$
$137$			0.184924i			0.0157991i	−0.999969	+	0.00789957i	$0.997485\pi$
$138$		0			0
$139$	−4.08707	−	4.08707i	−0.346661	−	0.346661i	0.512203	−	0.858864i	$-0.328829\pi$
$139$	−4.08707	−	4.08707i	−0.346661	−	0.346661i	−0.858864	+	0.512203i	$0.828829\pi$
$140$		0			0
$141$	−9.48797	+	9.48797i	−0.799031	+	0.799031i
$142$		0			0
$143$	−9.49073			−0.793654
$144$		0			0
$145$	−7.49940			−0.622791
$146$		0			0
$147$	2.04137	−	2.04137i	0.168369	−	0.168369i
$148$		0			0
$149$	−5.37041	−	5.37041i	−0.439961	−	0.439961i	0.452038	−	0.891999i	$-0.350697\pi$
$149$	−5.37041	−	5.37041i	−0.439961	−	0.439961i	−0.891999	+	0.452038i	$0.850697\pi$
$150$		0			0
$151$			11.4266i			0.929880i	0.885342	+	0.464940i	$0.153924\pi$
$151$			11.4266i			0.929880i	−0.885342	+	0.464940i	$0.846076\pi$
$152$		0			0
$153$			36.9697i			2.98882i
$154$		0			0
$155$	−3.67458	−	3.67458i	−0.295150	−	0.295150i
$156$		0			0
$157$	9.41825	−	9.41825i	0.751658	−	0.751658i	−0.223131	−	0.974789i	$-0.571628\pi$
$157$	9.41825	−	9.41825i	0.751658	−	0.751658i	0.974789	+	0.223131i	$0.0716276\pi$
$158$		0			0
$159$	−29.5913			−2.34674
$160$		0			0
$161$	−2.05612			−0.162045
$162$		0			0
$163$	12.4770	−	12.4770i	0.977270	−	0.977270i	−0.0224770	−	0.999747i	$-0.507155\pi$
$163$	12.4770	−	12.4770i	0.977270	−	0.977270i	0.999747	+	0.0224770i	$0.00715525\pi$
$164$		0			0
$165$	6.93210	+	6.93210i	0.539664	+	0.539664i
$166$		0			0
$167$		−	16.0783i		−	1.24418i	−0.782947	−	0.622088i	$-0.786284\pi$
$167$		−	16.0783i		−	1.24418i	0.782947	−	0.622088i	$-0.213716\pi$
$168$		0			0
$169$			5.30908i			0.408391i
$170$		0			0
$171$	7.41200	+	7.41200i	0.566809	+	0.566809i
$172$		0			0
$173$	14.4256	−	14.4256i	1.09676	−	1.09676i	0.101973	−	0.994787i	$-0.467485\pi$
$173$	14.4256	−	14.4256i	1.09676	−	1.09676i	0.994787	−	0.101973i	$-0.0325154\pi$
$174$		0			0
$175$	−4.01538			−0.303534
$176$		0			0
$177$	35.0318			2.63315
$178$		0			0
$179$	3.32674	−	3.32674i	0.248652	−	0.248652i	−0.571765	−	0.820417i	$-0.693741\pi$
$179$	3.32674	−	3.32674i	0.248652	−	0.248652i	0.820417	+	0.571765i	$0.193741\pi$
$180$		0			0
$181$	10.2899	+	10.2899i	0.764846	+	0.764846i	0.977194	−	0.212348i	$-0.0681112\pi$
$181$	10.2899	+	10.2899i	0.764846	+	0.764846i	−0.212348	+	0.977194i	$0.568111\pi$
$182$		0			0
$183$			11.4930i			0.849586i
$184$		0			0
$185$			9.23930i			0.679287i
$186$		0			0
$187$	−16.7710	−	16.7710i	−1.22642	−	1.22642i
$188$		0			0
$189$	4.76526	−	4.76526i	0.346622	−	0.346622i
$190$		0			0
$191$	26.6094			1.92539			0.962693	−	0.270595i	$-0.0872203\pi$
$191$	26.6094			1.92539			0.962693	+	0.270595i	$0.0872203\pi$
$192$		0			0
$193$	−25.2624			−1.81843			−0.909215	−	0.416327i	$-0.863317\pi$
$193$	−25.2624			−1.81843			−0.909215	+	0.416327i	$0.863317\pi$
$194$		0			0
$195$	−5.61751	+	5.61751i	−0.402278	+	0.402278i
$196$		0			0
$197$	−6.96551	−	6.96551i	−0.496272	−	0.496272i	0.414003	−	0.910275i	$-0.364130\pi$
$197$	−6.96551	−	6.96551i	−0.496272	−	0.496272i	−0.910275	+	0.414003i	$0.864130\pi$
$198$		0			0
$199$		−	15.2541i		−	1.08133i	−0.841238	−	0.540666i	$-0.818172\pi$
$199$		−	15.2541i		−	1.08133i	0.841238	−	0.540666i	$-0.181828\pi$
$200$		0			0
$201$		−	37.0385i		−	2.61249i
$202$		0			0
$203$	−5.34414	−	5.34414i	−0.375085	−	0.375085i
$204$		0			0
$205$	−0.666423	+	0.666423i	−0.0465450	+	0.0465450i
$206$		0			0
$207$	−10.9680			−0.762332
$208$		0			0
$209$	−6.72480			−0.465164
$210$		0			0
$211$	2.46973	−	2.46973i	0.170023	−	0.170023i	−0.616966	−	0.786990i	$-0.711639\pi$
$211$	2.46973	−	2.46973i	0.170023	−	0.170023i	0.786990	+	0.616966i	$0.211639\pi$
$212$		0			0
$213$	7.35933	+	7.35933i	0.504253	+	0.504253i
$214$		0			0
$215$		−	8.35442i		−	0.569767i
$216$		0			0
$217$		−	5.23708i		−	0.355516i
$218$		0			0
$219$	13.3338	+	13.3338i	0.901013	+	0.901013i
$220$		0			0
$221$	13.5906	−	13.5906i	0.914203	−	0.914203i
$222$		0			0
$223$	12.2245			0.818610			0.409305	−	0.912398i	$-0.365771\pi$
$223$	12.2245			0.818610			0.409305	+	0.912398i	$0.365771\pi$
$224$		0			0
$225$	−21.4194			−1.42796
$226$		0			0
$227$	−10.6687	+	10.6687i	−0.708107	+	0.708107i	−0.966137	−	0.258030i	$-0.916927\pi$
$227$	−10.6687	+	10.6687i	−0.708107	+	0.708107i	0.258030	+	0.966137i	$0.416927\pi$
$228$		0			0
$229$	−6.75289	−	6.75289i	−0.446244	−	0.446244i	0.447860	−	0.894104i	$-0.352186\pi$
$229$	−6.75289	−	6.75289i	−0.446244	−	0.446244i	−0.894104	+	0.447860i	$0.852186\pi$
$230$		0			0
$231$			9.87975i			0.650040i
$232$		0			0
$233$		−	7.42241i		−	0.486258i	−0.969994	−	0.243129i	$-0.921826\pi$
$233$		−	7.42241i		−	0.486258i	0.969994	−	0.243129i	$-0.0781739\pi$
$234$		0			0
$235$	−3.26115	−	3.26115i	−0.212734	−	0.212734i
$236$		0			0
$237$	−28.1339	+	28.1339i	−1.82749	+	1.82749i
$238$		0			0
$239$	3.44262			0.222685			0.111342	−	0.993782i	$-0.464485\pi$
$239$	3.44262			0.222685			0.111342	+	0.993782i	$0.464485\pi$
$240$		0			0
$241$	23.0386			1.48404			0.742022	−	0.670376i	$-0.233867\pi$
$241$	23.0386			1.48404			0.742022	+	0.670376i	$0.233867\pi$
$242$		0			0
$243$	−7.24852	+	7.24852i	−0.464993	+	0.464993i
$244$		0			0
$245$	0.701647	+	0.701647i	0.0448266	+	0.0448266i
$246$		0			0
$247$		−	5.44952i		−	0.346744i
$248$		0			0
$249$			18.3466i			1.16267i
$250$		0			0
$251$	−12.0833	−	12.0833i	−0.762690	−	0.762690i	0.214118	−	0.976808i	$-0.431312\pi$
$251$	−12.0833	−	12.0833i	−0.762690	−	0.762690i	−0.976808	+	0.214118i	$0.931312\pi$
$252$		0			0
$253$	4.97557	−	4.97557i	0.312812	−	0.312812i
$254$		0			0
$255$	−19.8534			−1.24327
$256$		0			0
$257$	2.15842			0.134638			0.0673191	−	0.997731i	$-0.478555\pi$
$257$	2.15842			0.134638			0.0673191	+	0.997731i	$0.478555\pi$
$258$		0			0
$259$	−6.58401	+	6.58401i	−0.409110	+	0.409110i
$260$		0			0
$261$	−28.5075	−	28.5075i	−1.76457	−	1.76457i
$262$		0			0
$263$			0.124319i			0.00766581i	0.999993	+	0.00383290i	$0.00122005\pi$
$263$			0.124319i			0.00766581i	−0.999993	+	0.00383290i	$0.998780\pi$
$264$		0			0
$265$		−	10.1710i		−	0.624797i
$266$		0			0
$267$	0.875390	+	0.875390i	0.0535730	+	0.0535730i
$268$		0			0
$269$	7.93651	−	7.93651i	0.483897	−	0.483897i	−0.422476	−	0.906374i	$-0.638839\pi$
$269$	7.93651	−	7.93651i	0.483897	−	0.483897i	0.906374	+	0.422476i	$0.138839\pi$
$270$		0			0
$271$	0.326600			0.0198395			0.00991976	−	0.999951i	$-0.496842\pi$
$271$	0.326600			0.0198395			0.00991976	+	0.999951i	$0.496842\pi$
$272$		0			0
$273$	−8.00617			−0.484556
$274$		0			0
$275$	9.71677	−	9.71677i	0.585944	−	0.585944i
$276$		0			0
$277$	−14.9992	−	14.9992i	−0.901214	−	0.901214i	0.0943269	−	0.995541i	$-0.469930\pi$
$277$	−14.9992	−	14.9992i	−0.901214	−	0.901214i	−0.995541	+	0.0943269i	$0.969930\pi$
$278$		0			0
$279$		−	27.9364i		−	1.67251i
$280$		0			0
$281$		−	27.8495i		−	1.66136i	−0.556750	−	0.830680i	$-0.687952\pi$
$281$		−	27.8495i		−	1.66136i	0.556750	−	0.830680i	$-0.312048\pi$
$282$		0			0
$283$	16.4548	+	16.4548i	0.978134	+	0.978134i	0.999766	−	0.0216317i	$-0.00688613\pi$
$283$	16.4548	+	16.4548i	0.978134	+	0.978134i	−0.0216317	+	0.999766i	$0.506886\pi$
$284$		0			0
$285$	−3.98037	+	3.98037i	−0.235777	+	0.235777i
$286$		0			0
$287$	−0.949797			−0.0560648
$288$		0			0
$289$	31.0318			1.82540
$290$		0			0
$291$	−29.8731	+	29.8731i	−1.75119	+	1.75119i
$292$		0			0
$293$	−20.0525	−	20.0525i	−1.17148	−	1.17148i	−0.981857	−	0.189624i	$-0.939273\pi$
$293$	−20.0525	−	20.0525i	−1.17148	−	1.17148i	−0.189624	−	0.981857i	$-0.560727\pi$
$294$		0			0
$295$			12.0409i			0.701051i
$296$		0			0
$297$			23.0628i			1.33824i
$298$		0			0
$299$	4.03201	+	4.03201i	0.233177	+	0.233177i
$300$		0			0
$301$	5.95343	−	5.95343i	0.343150	−	0.343150i
$302$		0			0
$303$	−45.7294			−2.62709
$304$		0			0
$305$	−3.95031			−0.226194
$306$		0			0
$307$	−18.8054	+	18.8054i	−1.07328	+	1.07328i	−0.0761901	+	0.997093i	$0.524276\pi$
$307$	−18.8054	+	18.8054i	−1.07328	+	1.07328i	−0.997093	+	0.0761901i	$0.975724\pi$
$308$		0			0
$309$	−37.6985	−	37.6985i	−2.14460	−	2.14460i
$310$		0			0
$311$		−	5.25843i		−	0.298178i	−0.988824	−	0.149089i	$-0.952366\pi$
$311$		−	5.25843i		−	0.298178i	0.988824	−	0.149089i	$-0.0476341\pi$
$312$		0			0
$313$			7.82442i			0.442262i	0.975244	+	0.221131i	$0.0709749\pi$
$313$			7.82442i			0.442262i	−0.975244	+	0.221131i	$0.929025\pi$
$314$		0			0
$315$	3.74283	+	3.74283i	0.210885	+	0.210885i
$316$		0			0
$317$	18.0890	−	18.0890i	1.01598	−	1.01598i	0.0161108	−	0.999870i	$-0.494872\pi$
$317$	18.0890	−	18.0890i	1.01598	−	1.01598i	0.999870	−	0.0161108i	$-0.00512846\pi$
$318$		0			0
$319$	25.8644			1.44813
$320$		0			0
$321$	−0.596777			−0.0333089
$322$		0			0
$323$	9.62983	−	9.62983i	0.535818	−	0.535818i
$324$		0			0
$325$	7.87410	+	7.87410i	0.436777	+	0.436777i
$326$		0			0
$327$		−	1.26325i		−	0.0698581i
$328$		0			0
$329$		−	4.64785i		−	0.256244i
$330$		0			0
$331$	0.702951	+	0.702951i	0.0386377	+	0.0386377i	0.726162	−	0.687524i	$-0.241302\pi$
$331$	0.702951	+	0.702951i	0.0386377	+	0.0386377i	−0.687524	+	0.726162i	$0.741302\pi$
$332$		0			0
$333$	−35.1214	+	35.1214i	−1.92464	+	1.92464i
$334$		0			0
$335$	12.7307			0.695551
$336$		0			0
$337$	13.4691			0.733710			0.366855	−	0.930278i	$-0.380434\pi$
$337$	13.4691			0.733710			0.366855	+	0.930278i	$0.380434\pi$
$338$		0			0
$339$	−34.1302	+	34.1302i	−1.85370	+	1.85370i
$340$		0			0
$341$	12.6731	+	12.6731i	0.686289	+	0.686289i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	5.89003i		−	0.317109i
$346$		0			0
$347$	−2.54293	−	2.54293i	−0.136512	−	0.136512i	0.635549	−	0.772061i	$-0.280774\pi$
$347$	−2.54293	−	2.54293i	−0.136512	−	0.136512i	−0.772061	+	0.635549i	$0.780774\pi$
$348$		0			0
$349$	−1.81167	+	1.81167i	−0.0969765	+	0.0969765i	−0.753931	−	0.656954i	$-0.771845\pi$
$349$	−1.81167	+	1.81167i	−0.0969765	+	0.0969765i	0.656954	+	0.753931i	$0.271845\pi$
$350$		0			0
$351$	−18.6892			−0.997556
$352$		0			0
$353$	−4.72060			−0.251252			−0.125626	−	0.992078i	$-0.540094\pi$
$353$	−4.72060			−0.251252			−0.125626	+	0.992078i	$0.540094\pi$
$354$		0			0
$355$	−2.52951	+	2.52951i	−0.134252	+	0.134252i
$356$		0			0
$357$	−14.1477	−	14.1477i	−0.748775	−	0.748775i
$358$		0			0
$359$		−	16.9233i		−	0.893177i	−0.894739	−	0.446589i	$-0.852639\pi$
$359$		−	16.9233i		−	0.893177i	0.894739	−	0.446589i	$-0.147361\pi$
$360$		0			0
$361$			15.1387i			0.796772i
$362$		0			0
$363$	−1.45287	−	1.45287i	−0.0762562	−	0.0762562i
$364$		0			0
$365$	−4.58301	+	4.58301i	−0.239886	+	0.239886i
$366$		0			0
$367$	−19.8872			−1.03810			−0.519051	−	0.854743i	$-0.673714\pi$
$367$	−19.8872			−1.03810			−0.519051	+	0.854743i	$0.673714\pi$
$368$		0			0
$369$	−5.06655			−0.263754
$370$		0			0
$371$	7.24791	−	7.24791i	0.376293	−	0.376293i
$372$		0			0
$373$	−6.84947	−	6.84947i	−0.354652	−	0.354652i	0.507185	−	0.861837i	$-0.330686\pi$
$373$	−6.84947	−	6.84947i	−0.354652	−	0.354652i	−0.861837	+	0.507185i	$0.830686\pi$
$374$		0			0
$375$		−	25.8258i		−	1.33364i
$376$		0			0
$377$			20.9595i			1.07947i
$378$		0			0
$379$	−11.9445	−	11.9445i	−0.613548	−	0.613548i	0.330320	−	0.943869i	$-0.392843\pi$
$379$	−11.9445	−	11.9445i	−0.613548	−	0.613548i	−0.943869	+	0.330320i	$0.892843\pi$
$380$		0			0
$381$	10.0362	−	10.0362i	0.514168	−	0.514168i
$382$		0			0
$383$	−24.7947			−1.26695			−0.633476	−	0.773763i	$-0.718372\pi$
$383$	−24.7947			−1.26695			−0.633476	+	0.773763i	$0.718372\pi$
$384$		0			0
$385$	−3.39582			−0.173067
$386$		0			0
$387$	31.7577	−	31.7577i	1.61433	−	1.61433i
$388$		0			0
$389$	−2.18643	−	2.18643i	−0.110857	−	0.110857i	0.649503	−	0.760359i	$-0.274977\pi$
$389$	−2.18643	−	2.18643i	−0.110857	−	0.110857i	−0.760359	+	0.649503i	$0.774977\pi$
$390$		0			0
$391$			14.2499i			0.720649i
$392$		0			0
$393$		−	4.50744i		−	0.227370i
$394$		0			0
$395$	−9.67004	−	9.67004i	−0.486553	−	0.486553i
$396$		0			0
$397$	0.272216	−	0.272216i	0.0136621	−	0.0136621i	−0.700243	−	0.713905i	$-0.746925\pi$
$397$	0.272216	−	0.272216i	0.0136621	−	0.0136621i	0.713905	+	0.700243i	$0.246925\pi$
$398$		0			0
$399$	−5.67289			−0.284000
$400$		0			0
$401$	−14.6370			−0.730937			−0.365468	−	0.930824i	$-0.619091\pi$
$401$	−14.6370			−0.730937			−0.365468	+	0.930824i	$0.619091\pi$
$402$		0			0
$403$	−10.2698	+	10.2698i	−0.511577	+	0.511577i
$404$		0			0
$405$	2.42225	+	2.42225i	0.120362	+	0.120362i
$406$		0			0
$407$		−	31.8651i		−	1.57950i
$408$		0			0
$409$		−	5.20342i		−	0.257292i	−0.991691	−	0.128646i	$-0.958937\pi$
$409$		−	5.20342i		−	0.257292i	0.991691	−	0.128646i	$-0.0410632\pi$
$410$		0			0
$411$	−0.377498	−	0.377498i	−0.0186206	−	0.0186206i
$412$		0			0
$413$	−8.58048	+	8.58048i	−0.422218	+	0.422218i
$414$		0			0
$415$	−6.30601			−0.309550
$416$		0			0
$417$	16.6864			0.817138
$418$		0			0
$419$	−9.91249	+	9.91249i	−0.484257	+	0.484257i	−0.906488	−	0.422231i	$-0.861247\pi$
$419$	−9.91249	+	9.91249i	−0.484257	+	0.484257i	0.422231	+	0.906488i	$0.361247\pi$
$420$		0			0
$421$	5.87543	+	5.87543i	0.286351	+	0.286351i	0.835635	−	0.549285i	$-0.185100\pi$
$421$	5.87543	+	5.87543i	0.286351	+	0.286351i	−0.549285	+	0.835635i	$0.685100\pi$
$422$		0			0
$423$		−	24.7933i		−	1.20549i
$424$		0			0
$425$			27.8286i			1.34989i
$426$		0			0
$427$	−2.81502	−	2.81502i	−0.136229	−	0.136229i
$428$		0			0
$429$	19.3740	−	19.3740i	0.935388	−	0.935388i
$430$		0			0
$431$	18.4777			0.890039			0.445019	−	0.895521i	$-0.353197\pi$
$431$	18.4777			0.890039			0.445019	+	0.895521i	$0.353197\pi$
$432$		0			0
$433$	8.69984			0.418088			0.209044	−	0.977906i	$-0.432965\pi$
$433$	8.69984			0.418088			0.209044	+	0.977906i	$0.432965\pi$
$434$		0			0
$435$	15.3090	−	15.3090i	0.734011	−	0.734011i
$436$		0			0
$437$	2.85694	+	2.85694i	0.136666	+	0.136666i
$438$		0			0
$439$			2.08886i			0.0996959i	0.998757	+	0.0498479i	$0.0158737\pi$
$439$			2.08886i			0.0996959i	−0.998757	+	0.0498479i	$0.984126\pi$
$440$		0			0
$441$			5.33435i			0.254017i
$442$		0			0
$443$	−1.57395	−	1.57395i	−0.0747808	−	0.0747808i	0.668727	−	0.743508i	$-0.266839\pi$
$443$	−1.57395	−	1.57395i	−0.0747808	−	0.0747808i	−0.743508	+	0.668727i	$0.766839\pi$
$444$		0			0
$445$	−0.300884	+	0.300884i	−0.0142633	+	0.0142633i
$446$		0			0
$447$	21.9260			1.03706
$448$		0			0
$449$	−22.6235			−1.06767			−0.533835	−	0.845589i	$-0.679250\pi$
$449$	−22.6235			−1.06767			−0.533835	+	0.845589i	$0.679250\pi$
$450$		0			0
$451$	2.29840	−	2.29840i	0.108228	−	0.108228i
$452$		0			0
$453$	−23.3258	−	23.3258i	−1.09594	−	1.09594i
$454$		0			0
$455$		−	2.75184i		−	0.129008i
$456$		0			0
$457$		−	22.9357i		−	1.07289i	−0.843937	−	0.536443i	$-0.819768\pi$
$457$		−	22.9357i		−	1.07289i	0.843937	−	0.536443i	$-0.180232\pi$
$458$		0			0
$459$	−33.0256	−	33.0256i	−1.54150	−	1.54150i
$460$		0			0
$461$	9.77472	−	9.77472i	0.455254	−	0.455254i	−0.441840	−	0.897094i	$-0.645674\pi$
$461$	9.77472	−	9.77472i	0.455254	−	0.455254i	0.897094	+	0.441840i	$0.145674\pi$
$462$		0			0
$463$	−22.4440			−1.04306			−0.521531	−	0.853233i	$-0.674639\pi$
$463$	−22.4440			−1.04306			−0.521531	+	0.853233i	$0.674639\pi$
$464$		0			0
$465$	15.0023			0.695717
$466$		0			0
$467$	−1.55804	+	1.55804i	−0.0720976	+	0.0720976i	−0.742236	−	0.670138i	$-0.766235\pi$
$467$	−1.55804	+	1.55804i	−0.0720976	+	0.0720976i	0.670138	+	0.742236i	$0.266235\pi$
$468$		0			0
$469$	9.07198	+	9.07198i	0.418905	+	0.418905i
$470$		0			0
$471$			38.4522i			1.77178i
$472$		0			0
$473$			28.8133i			1.32484i
$474$		0			0
$475$	5.57931	+	5.57931i	0.255996	+	0.255996i
$476$		0			0
$477$	38.6629	−	38.6629i	1.77025	−	1.77025i
$478$		0			0
$479$	36.0952			1.64923			0.824615	−	0.565694i	$-0.191392\pi$
$479$	36.0952			1.64923			0.824615	+	0.565694i	$0.191392\pi$
$480$		0			0
$481$	25.8223			1.17739
$482$		0			0
$483$	4.19729	−	4.19729i	0.190983	−	0.190983i
$484$		0			0
$485$	−10.2678	−	10.2678i	−0.466237	−	0.466237i
$486$		0			0
$487$			40.4748i			1.83409i	0.398785	+	0.917044i	$0.369432\pi$
$487$			40.4748i			1.83409i	−0.398785	+	0.917044i	$0.630568\pi$
$488$		0			0
$489$			50.9400i			2.30359i
$490$		0			0
$491$	−27.1284	−	27.1284i	−1.22429	−	1.22429i	−0.966094	−	0.258192i	$-0.916873\pi$
$491$	−27.1284	−	27.1284i	−1.22429	−	1.22429i	−0.258192	−	0.966094i	$-0.583127\pi$
$492$		0			0
$493$	−37.0375	+	37.0375i	−1.66809	+	1.66809i
$494$		0			0
$495$	−18.1145			−0.814185
$496$		0			0
$497$	−3.60510			−0.161711
$498$		0			0
$499$	−1.38687	+	1.38687i	−0.0620847	+	0.0620847i	−0.737467	−	0.675383i	$-0.763978\pi$
$499$	−1.38687	+	1.38687i	−0.0620847	+	0.0620847i	0.675383	+	0.737467i	$0.263978\pi$
$500$		0			0
$501$	32.8217	+	32.8217i	1.46637	+	1.46637i
$502$		0			0
$503$		−	16.6445i		−	0.742140i	−0.928605	−	0.371070i	$-0.878991\pi$
$503$		−	16.6445i		−	0.742140i	0.928605	−	0.371070i	$-0.121009\pi$
$504$		0			0
$505$		−	15.7179i		−	0.699436i
$506$		0			0
$507$	−10.8378	−	10.8378i	−0.481322	−	0.481322i
$508$		0			0
$509$	17.4276	−	17.4276i	0.772463	−	0.772463i	−0.206074	−	0.978536i	$-0.566069\pi$
$509$	17.4276	−	17.4276i	0.772463	−	0.772463i	0.978536	+	0.206074i	$0.0660686\pi$
$510$		0			0
$511$	−6.53179			−0.288949
$512$		0			0
$513$	−13.2425			−0.584671
$514$		0			0
$515$	12.9575	−	12.9575i	0.570978	−	0.570978i
$516$		0			0
$517$	11.2473	+	11.2473i	0.494655	+	0.494655i
$518$		0			0
$519$			58.8960i			2.58525i
$520$		0			0
$521$		−	2.69192i		−	0.117935i	−0.998260	−	0.0589676i	$-0.981219\pi$
$521$		−	2.69192i		−	0.117935i	0.998260	−	0.0589676i	$-0.0187809\pi$
$522$		0			0
$523$	10.9962	+	10.9962i	0.480830	+	0.480830i	0.905397	−	0.424566i	$-0.139573\pi$
$523$	10.9962	+	10.9962i	0.480830	+	0.480830i	−0.424566	+	0.905397i	$0.639573\pi$
$524$		0			0
$525$	8.19686	−	8.19686i	0.357740	−	0.357740i
$526$		0			0
$527$	−36.2956			−1.58106
$528$		0			0
$529$	18.7724			0.816191
$530$		0			0
$531$	−45.7713	+	45.7713i	−1.98630	+	1.98630i
$532$		0			0
$533$	1.86254	+	1.86254i	0.0806755	+	0.0806755i
$534$		0			0
$535$		−	0.205121i		−	0.00886816i
$536$		0			0
$537$			13.5822i			0.586115i
$538$		0			0
$539$	−2.41989	−	2.41989i	−0.104232	−	0.104232i
$540$		0			0
$541$	−6.46720	+	6.46720i	−0.278047	+	0.278047i	−0.832329	−	0.554282i	$-0.812993\pi$
$541$	−6.46720	+	6.46720i	−0.278047	+	0.278047i	0.554282	+	0.832329i	$0.312993\pi$
$542$		0			0
$543$	−42.0111			−1.80287
$544$		0			0
$545$	0.434199			0.0185990
$546$		0			0
$547$	−20.5089	+	20.5089i	−0.876896	+	0.876896i	−0.993212	−	0.116316i	$-0.962891\pi$
$547$	−20.5089	+	20.5089i	−0.876896	+	0.876896i	0.116316	+	0.993212i	$0.462891\pi$
$548$		0			0
$549$	−15.0163	−	15.0163i	−0.640881	−	0.640881i
$550$		0			0
$551$			14.8512i			0.632682i
$552$		0			0
$553$		−	13.7819i		−	0.586066i
$554$		0			0
$555$	−18.8608	−	18.8608i	−0.800596	−	0.800596i
$556$		0			0
$557$	11.0551	−	11.0551i	0.468421	−	0.468421i	−0.432981	−	0.901403i	$-0.642538\pi$
$557$	11.0551	−	11.0551i	0.468421	−	0.468421i	0.901403	+	0.432981i	$0.142538\pi$
$558$		0			0
$559$	−23.3492			−0.987565
$560$		0			0
$561$	68.4716			2.89087
$562$		0			0
$563$	15.3790	−	15.3790i	0.648147	−	0.648147i	−0.304398	−	0.952545i	$-0.598455\pi$
$563$	15.3790	−	15.3790i	0.648147	−	0.648147i	0.952545	+	0.304398i	$0.0984552\pi$
$564$		0			0
$565$	−11.7310	−	11.7310i	−0.493529	−	0.493529i
$566$		0			0
$567$			3.45223i			0.144980i
$568$		0			0
$569$			9.21322i			0.386238i	0.981175	+	0.193119i	$0.0618604\pi$
$569$			9.21322i			0.386238i	−0.981175	+	0.193119i	$0.938140\pi$
$570$		0			0
$571$	10.3471	+	10.3471i	0.433014	+	0.433014i	0.889653	−	0.456638i	$-0.150947\pi$
$571$	10.3471	+	10.3471i	0.433014	+	0.433014i	−0.456638	+	0.889653i	$0.650947\pi$
$572$		0			0
$573$	−54.3195	+	54.3195i	−2.26923	+	2.26923i
$574$		0			0
$575$	−8.25609			−0.344303
$576$		0			0
$577$	2.75852			0.114839			0.0574193	−	0.998350i	$-0.481713\pi$
$577$	2.75852			0.114839			0.0574193	+	0.998350i	$0.481713\pi$
$578$		0			0
$579$	51.5699	−	51.5699i	2.14317	−	2.14317i
$580$		0			0
$581$	−4.49372	−	4.49372i	−0.186431	−	0.186431i
$582$		0			0
$583$			35.0783i			1.45279i
$584$		0			0
$585$		−	14.6793i		−	0.606913i
$586$		0			0
$587$	−4.18689	−	4.18689i	−0.172812	−	0.172812i	0.615402	−	0.788213i	$-0.288994\pi$
$587$	−4.18689	−	4.18689i	−0.172812	−	0.172812i	−0.788213	+	0.615402i	$0.788994\pi$
$588$		0			0
$589$	−7.27684	+	7.27684i	−0.299837	+	0.299837i
$590$		0			0
$591$	28.4383			1.16980
$592$		0			0
$593$	−3.11656			−0.127982			−0.0639908	−	0.997950i	$-0.520383\pi$
$593$	−3.11656			−0.127982			−0.0639908	+	0.997950i	$0.520383\pi$
$594$		0			0
$595$	4.86277	−	4.86277i	0.199354	−	0.199354i
$596$		0			0
$597$	31.1391	+	31.1391i	1.27444	+	1.27444i
$598$		0			0
$599$		−	5.12382i		−	0.209354i	−0.994506	−	0.104677i	$-0.966619\pi$
$599$		−	5.12382i		−	0.209354i	0.994506	−	0.104677i	$-0.0333808\pi$
$600$		0			0
$601$			28.1920i			1.14997i	0.818162	+	0.574987i	$0.194993\pi$
$601$			28.1920i			1.14997i	−0.818162	+	0.574987i	$0.805007\pi$
$602$		0			0
$603$	48.3931	+	48.3931i	1.97072	+	1.97072i
$604$		0			0
$605$	0.499374	−	0.499374i	0.0203025	−	0.0203025i
$606$		0			0
$607$	40.0403			1.62518			0.812592	−	0.582832i	$-0.198056\pi$
$607$	40.0403			1.62518			0.812592	+	0.582832i	$0.198056\pi$
$608$		0			0
$609$	21.8187			0.884137
$610$		0			0
$611$	−9.11437	+	9.11437i	−0.368728	+	0.368728i
$612$		0			0
$613$	12.6820	+	12.6820i	0.512222	+	0.512222i	0.915207	−	0.402985i	$-0.132027\pi$
$613$	12.6820	+	12.6820i	0.512222	+	0.512222i	−0.402985	+	0.915207i	$0.632027\pi$
$614$		0			0
$615$		−	2.72083i		−	0.109714i
$616$		0			0
$617$			35.2965i			1.42098i	0.703706	+	0.710491i	$0.251527\pi$
$617$			35.2965i			1.42098i	−0.703706	+	0.710491i	$0.748473\pi$
$618$		0			0
$619$	−6.40966	−	6.40966i	−0.257626	−	0.257626i	0.566462	−	0.824088i	$-0.308312\pi$
$619$	−6.40966	−	6.40966i	−0.257626	−	0.257626i	−0.824088	+	0.566462i	$0.808312\pi$
$620$		0			0
$621$	9.79793	−	9.79793i	0.393177	−	0.393177i
$622$		0			0
$623$	−0.428825			−0.0171805
$624$		0			0
$625$	−11.2002			−0.448008
$626$		0			0
$627$	13.7278	−	13.7278i	0.548234	−	0.548234i
$628$		0			0
$629$	45.6305	+	45.6305i	1.81941	+	1.81941i
$630$		0			0
$631$		−	8.85344i		−	0.352450i	−0.984350	−	0.176225i	$-0.943611\pi$
$631$		−	8.85344i		−	0.352450i	0.984350	−	0.176225i	$-0.0563886\pi$
$632$		0			0
$633$			10.0832i			0.400773i
$634$		0			0
$635$	3.44957	+	3.44957i	0.136892	+	0.136892i
$636$		0			0
$637$	1.96098	−	1.96098i	0.0776970	−	0.0776970i
$638$		0			0
$639$	−19.2309			−0.760761
$640$		0			0
$641$	−0.523959			−0.0206951			−0.0103476	−	0.999946i	$-0.503294\pi$
$641$	−0.523959			−0.0206951			−0.0103476	+	0.999946i	$0.503294\pi$
$642$		0			0
$643$	−7.52914	+	7.52914i	−0.296920	+	0.296920i	−0.839806	−	0.542886i	$-0.817332\pi$
$643$	−7.52914	+	7.52914i	−0.296920	+	0.296920i	0.542886	+	0.839806i	$0.317332\pi$
$644$		0			0
$645$	17.0544	+	17.0544i	0.671517	+	0.671517i
$646$		0			0
$647$			17.9059i			0.703955i	0.936009	+	0.351977i	$0.114491\pi$
$647$			17.9059i			0.703955i	−0.936009	+	0.351977i	$0.885509\pi$
$648$		0			0
$649$		−	41.5276i		−	1.63010i
$650$		0			0
$651$	10.6908	+	10.6908i	0.419005	+	0.419005i
$652$		0			0
$653$	−7.60327	+	7.60327i	−0.297539	+	0.297539i	−0.840049	−	0.542510i	$-0.817474\pi$
$653$	−7.60327	+	7.60327i	−0.297539	+	0.297539i	0.542510	+	0.840049i	$0.317474\pi$
$654$		0			0
$655$	1.54927			0.0605351
$656$		0			0
$657$	−34.8428			−1.35935
$658$		0			0
$659$	12.7271	−	12.7271i	0.495776	−	0.495776i	−0.414344	−	0.910120i	$-0.635989\pi$
$659$	12.7271	−	12.7271i	0.495776	−	0.495776i	0.910120	+	0.414344i	$0.135989\pi$
$660$		0			0
$661$	−22.3267	−	22.3267i	−0.868410	−	0.868410i	0.123887	−	0.992296i	$-0.460464\pi$
$661$	−22.3267	−	22.3267i	−0.868410	−	0.868410i	−0.992296	+	0.123887i	$0.960464\pi$
$662$		0			0
$663$			55.4868i			2.15493i
$664$		0			0
$665$		−	1.94986i		−	0.0756122i
$666$		0			0
$667$	−10.9882	−	10.9882i	−0.425464	−	0.425464i
$668$		0			0
$669$	−24.9546	+	24.9546i	−0.964800	+	0.964800i
$670$		0			0
$671$	13.6241			0.525952
$672$		0			0
$673$	−29.7030			−1.14497			−0.572483	−	0.819917i	$-0.694020\pi$
$673$	−29.7030			−1.14497			−0.572483	+	0.819917i	$0.694020\pi$
$674$		0			0
$675$	19.1343	−	19.1343i	0.736481	−	0.736481i
$676$		0			0
$677$	−1.03778	−	1.03778i	−0.0398853	−	0.0398853i	0.686883	−	0.726768i	$-0.258979\pi$
$677$	−1.03778	−	1.03778i	−0.0398853	−	0.0398853i	−0.726768	+	0.686883i	$0.758979\pi$
$678$		0			0
$679$		−	14.6339i		−	0.561596i
$680$		0			0
$681$		−	43.5575i		−	1.66913i
$682$		0			0
$683$	5.91035	+	5.91035i	0.226153	+	0.226153i	0.811084	−	0.584930i	$-0.198878\pi$
$683$	5.91035	+	5.91035i	0.226153	+	0.226153i	−0.584930	+	0.811084i	$0.698878\pi$
$684$		0			0
$685$	0.129752	−	0.129752i	0.00495755	−	0.00495755i
$686$		0			0
$687$	27.5702			1.05187
$688$		0			0
$689$	−28.4261			−1.08295
$690$		0			0
$691$	6.31513	−	6.31513i	0.240239	−	0.240239i	−0.576710	−	0.816949i	$-0.695664\pi$
$691$	6.31513	−	6.31513i	0.240239	−	0.240239i	0.816949	+	0.576710i	$0.195664\pi$
$692$		0			0
$693$	−12.9085	−	12.9085i	−0.490354	−	0.490354i
$694$		0			0
$695$			5.73537i			0.217555i
$696$		0			0
$697$			6.58257i			0.249333i
$698$		0			0
$699$	15.1519	+	15.1519i	0.573096	+	0.573096i
$700$		0			0
$701$	35.3526	−	35.3526i	1.33525	−	1.33525i	0.434647	−	0.900601i	$-0.356873\pi$
$701$	35.3526	−	35.3526i	1.33525	−	1.33525i	0.900601	−	0.434647i	$-0.143127\pi$
$702$		0			0
$703$	18.2968			0.690075
$704$		0			0
$705$	13.3144			0.501450
$706$		0			0
$707$	11.2007	−	11.2007i	0.421245	−	0.421245i
$708$		0			0
$709$	25.6099	+	25.6099i	0.961801	+	0.961801i	0.999297	−	0.0374956i	$-0.0119380\pi$
$709$	25.6099	+	25.6099i	0.961801	+	0.961801i	−0.0374956	+	0.999297i	$0.511938\pi$
$710$		0			0
$711$		−	73.5175i		−	2.75712i
$712$		0			0
$713$		−	10.7680i		−	0.403267i
$714$		0			0
$715$	6.65914	+	6.65914i	0.249038	+	0.249038i
$716$		0			0
$717$	−7.02764	+	7.02764i	−0.262452	+	0.262452i
$718$		0			0
$719$	−12.8390			−0.478816			−0.239408	−	0.970919i	$-0.576953\pi$
$719$	−12.8390			−0.478816			−0.239408	+	0.970919i	$0.576953\pi$
$720$		0			0
$721$	18.4673			0.687759
$722$		0			0
$723$	−47.0301	+	47.0301i	−1.74907	+	1.74907i
$724$		0			0
$725$	−21.4588	−	21.4588i	−0.796958	−	0.796958i
$726$		0			0
$727$		−	50.1537i		−	1.86010i	−0.367436	−	0.930049i	$-0.619764\pi$
$727$		−	50.1537i		−	1.86010i	0.367436	−	0.930049i	$-0.380236\pi$
$728$		0			0
$729$		−	39.9504i		−	1.47965i
$730$		0			0
$731$	−41.2602	−	41.2602i	−1.52607	−	1.52607i
$732$		0			0
$733$	−21.4286	+	21.4286i	−0.791485	+	0.791485i	−0.981736	−	0.190250i	$-0.939070\pi$
$733$	−21.4286	+	21.4286i	−0.791485	+	0.791485i	0.190250	+	0.981736i	$0.439070\pi$
$734$		0			0
$735$	−2.86464			−0.105664
$736$		0			0
$737$	−43.9064			−1.61731
$738$		0			0
$739$	2.36694	−	2.36694i	0.0870693	−	0.0870693i	−0.662231	−	0.749300i	$-0.730390\pi$
$739$	2.36694	−	2.36694i	0.0870693	−	0.0870693i	0.749300	+	0.662231i	$0.230390\pi$
$740$		0			0
$741$	11.1245	+	11.1245i	0.408667	+	0.408667i
$742$		0			0
$743$		−	4.56306i		−	0.167403i	−0.996491	−	0.0837013i	$-0.973326\pi$
$743$		−	4.56306i		−	0.167403i	0.996491	−	0.0837013i	$-0.0266742\pi$
$744$		0			0
$745$			7.53627i			0.276108i
$746$		0			0
$747$	−23.9711	−	23.9711i	−0.877055	−	0.877055i
$748$		0			0
$749$	0.146171	−	0.146171i	0.00534097	−	0.00534097i
$750$		0			0
$751$	6.04590			0.220618			0.110309	−	0.993897i	$-0.464816\pi$
$751$	6.04590			0.220618			0.110309	+	0.993897i	$0.464816\pi$
$752$		0			0
$753$	49.3328			1.79779
$754$		0			0
$755$	8.01741	−	8.01741i	0.291784	−	0.291784i
$756$		0			0
$757$	−25.0992	−	25.0992i	−0.912244	−	0.912244i	0.0842043	−	0.996449i	$-0.473165\pi$
$757$	−25.0992	−	25.0992i	−0.912244	−	0.912244i	−0.996449	+	0.0842043i	$0.973165\pi$
$758$		0			0
$759$			20.3139i			0.737349i
$760$		0			0
$761$			16.2508i			0.589089i	0.955638	+	0.294545i	$0.0951680\pi$
$761$			16.2508i			0.589089i	−0.955638	+	0.294545i	$0.904832\pi$
$762$		0			0
$763$	0.309414	+	0.309414i	0.0112015	+	0.0112015i
$764$		0			0
$765$	25.9397	−	25.9397i	0.937852	−	0.937852i
$766$		0			0
$767$	33.6524			1.21512
$768$		0			0
$769$	−18.6812			−0.673660			−0.336830	−	0.941565i	$-0.609355\pi$
$769$	−18.6812			−0.673660			−0.336830	+	0.941565i	$0.609355\pi$
$770$		0			0
$771$	−4.40612	+	4.40612i	−0.158682	+	0.158682i
$772$		0			0
$773$	−10.6288	−	10.6288i	−0.382293	−	0.382293i	0.489635	−	0.871928i	$-0.337130\pi$
$773$	−10.6288	−	10.6288i	−0.382293	−	0.382293i	−0.871928	+	0.489635i	$0.837130\pi$
$774$		0			0
$775$		−	21.0289i		−	0.755380i
$776$		0			0
$777$		−	26.8807i		−	0.964341i
$778$		0			0
$779$	1.31973	+	1.31973i	0.0472842	+	0.0472842i
$780$		0			0
$781$	8.72394	−	8.72394i	0.312167	−	0.312167i
$782$		0			0
$783$	50.9324			1.82018
$784$		0			0
$785$	−13.2166			−0.471720
$786$		0			0
$787$	17.1899	−	17.1899i	0.612755	−	0.612755i	−0.330908	−	0.943663i	$-0.607355\pi$
$787$	17.1899	−	17.1899i	0.612755	−	0.612755i	0.943663	+	0.330908i	$0.107355\pi$
$788$		0			0
$789$	−0.253780	−	0.253780i	−0.00903479	−	0.00903479i
$790$		0			0
$791$		−	16.7193i		−	0.594470i
$792$		0			0
$793$			11.0404i			0.392058i
$794$		0			0
$795$	20.7626	+	20.7626i	0.736375	+	0.736375i
$796$		0			0
$797$	19.5801	−	19.5801i	0.693561	−	0.693561i	−0.269453	−	0.963014i	$-0.586843\pi$
$797$	19.5801	−	19.5801i	0.693561	−	0.693561i	0.963014	+	0.269453i	$0.0868427\pi$
$798$		0			0
$799$	−32.2120			−1.13958
$800$		0			0
$801$	−2.28750			−0.0808250
$802$		0			0
$803$	15.8062	−	15.8062i	0.557789	−	0.557789i
$804$		0			0
$805$	1.44267	+	1.44267i	0.0508474	+	0.0508474i
$806$		0			0
$807$			32.4026i			1.14063i
$808$		0			0
$809$			52.7688i			1.85525i	0.373511	+	0.927626i	$0.378154\pi$
$809$			52.7688i			1.85525i	−0.373511	+	0.927626i	$0.621846\pi$
$810$		0			0
$811$	−10.0534	−	10.0534i	−0.353024	−	0.353024i	0.508210	−	0.861233i	$-0.330307\pi$
$811$	−10.0534	−	10.0534i	−0.353024	−	0.353024i	−0.861233	+	0.508210i	$0.830307\pi$
$812$		0			0
$813$	−0.666709	+	0.666709i	−0.0233825	+	0.0233825i
$814$		0			0
$815$	−17.5088			−0.613308
$816$		0			0
$817$	−16.5444			−0.578815
$818$		0			0
$819$	10.4606	−	10.4606i	0.365522	−	0.365522i
$820$		0			0
$821$	−4.10780	−	4.10780i	−0.143363	−	0.143363i	0.631782	−	0.775146i	$-0.282324\pi$
$821$	−4.10780	−	4.10780i	−0.143363	−	0.143363i	−0.775146	+	0.631782i	$0.782324\pi$
$822$		0			0
$823$		−	23.4496i		−	0.817403i	−0.912668	−	0.408702i	$-0.865982\pi$
$823$		−	23.4496i		−	0.817403i	0.912668	−	0.408702i	$-0.134018\pi$
$824$		0			0
$825$			39.6710i			1.38117i
$826$		0			0
$827$	33.3518	+	33.3518i	1.15976	+	1.15976i	0.984528	+	0.175228i	$0.0560661\pi$
$827$	33.3518	+	33.3518i	1.15976	+	1.15976i	0.175228	+	0.984528i	$0.443934\pi$
$828$		0			0
$829$	−21.5208	+	21.5208i	−0.747449	+	0.747449i	−0.973999	−	0.226550i	$-0.927255\pi$
$829$	−21.5208	+	21.5208i	−0.747449	+	0.747449i	0.226550	+	0.973999i	$0.427255\pi$
$830$		0			0
$831$	61.2377			2.12431
$832$		0			0
$833$	6.93050			0.240128
$834$		0			0
$835$	−11.2813	+	11.2813i	−0.390406	+	0.390406i
$836$		0			0
$837$	24.9560	+	24.9560i	0.862607	+	0.862607i
$838$		0			0
$839$		−	36.6874i		−	1.26659i	−0.773911	−	0.633295i	$-0.781702\pi$
$839$		−	36.6874i		−	1.26659i	0.773911	−	0.633295i	$-0.218298\pi$
$840$		0			0
$841$		−	28.1196i		−	0.969642i
$842$		0			0
$843$	56.8510	+	56.8510i	1.95805	+	1.95805i
$844$		0			0
$845$	3.72510	−	3.72510i	0.128147	−	0.128147i
$846$		0			0
$847$	0.711717			0.0244549
$848$		0			0
$849$	−67.1804			−2.30562
$850$		0			0
$851$	−13.5375	+	13.5375i	−0.464059	+	0.464059i
$852$		0			0
$853$	6.01880	+	6.01880i	0.206080	+	0.206080i	0.802599	−	0.596519i	$-0.203450\pi$
$853$	6.01880	+	6.01880i	0.206080	+	0.206080i	−0.596519	+	0.802599i	$0.703450\pi$
$854$		0			0
$855$		−	10.4012i		−	0.355714i
$856$		0			0
$857$		−	54.0539i		−	1.84645i	−0.384266	−	0.923223i	$-0.625545\pi$
$857$		−	54.0539i		−	1.84645i	0.384266	−	0.923223i	$-0.374455\pi$
$858$		0			0
$859$	20.1054	+	20.1054i	0.685986	+	0.685986i	0.961342	−	0.275356i	$-0.0887957\pi$
$859$	20.1054	+	20.1054i	0.685986	+	0.685986i	−0.275356	+	0.961342i	$0.588796\pi$
$860$		0			0
$861$	1.93888	−	1.93888i	0.0660770	−	0.0660770i
$862$		0			0
$863$	−11.1553			−0.379732			−0.189866	−	0.981810i	$-0.560805\pi$
$863$	−11.1553			−0.379732			−0.189866	+	0.981810i	$0.560805\pi$
$864$		0			0
$865$	−20.2434			−0.688296
$866$		0			0
$867$	−63.3473	+	63.3473i	−2.15139	+	2.15139i
$868$		0			0
$869$	33.3507	+	33.3507i	1.13134	+	1.13134i
$870$		0			0
$871$		−	35.5800i		−	1.20558i
$872$		0			0
$873$		−	78.0621i		−	2.64200i
$874$		0			0
$875$	6.32562	+	6.32562i	0.213845	+	0.213845i
$876$		0			0
$877$	23.1457	−	23.1457i	0.781575	−	0.781575i	−0.198522	−	0.980097i	$-0.563614\pi$
$877$	23.1457	−	23.1457i	0.781575	−	0.781575i	0.980097	+	0.198522i	$0.0636140\pi$
$878$		0			0
$879$	81.8691			2.76138
$880$		0			0
$881$	−22.2981			−0.751244			−0.375622	−	0.926773i	$-0.622571\pi$
$881$	−22.2981			−0.751244			−0.375622	+	0.926773i	$0.622571\pi$
$882$		0			0
$883$	20.3610	−	20.3610i	0.685203	−	0.685203i	−0.275965	−	0.961168i	$-0.588997\pi$
$883$	20.3610	−	20.3610i	0.685203	−	0.685203i	0.961168	+	0.275965i	$0.0889973\pi$
$884$		0			0
$885$	−24.5800	−	24.5800i	−0.826247	−	0.826247i
$886$		0			0
$887$		−	40.1793i		−	1.34909i	−0.738234	−	0.674544i	$-0.764340\pi$
$887$		−	40.1793i		−	1.34909i	0.738234	−	0.674544i	$-0.235660\pi$
$888$		0			0
$889$			4.91639i			0.164891i
$890$		0			0
$891$	−8.35400	−	8.35400i	−0.279870	−	0.279870i
$892$		0			0
$893$	−6.45812	+	6.45812i	−0.216113	+	0.216113i
$894$		0			0
$895$	−4.66840			−0.156047
$896$		0			0
$897$	−16.4616			−0.549638
$898$		0			0
$899$	27.9877	−	27.9877i	0.933441	−	0.933441i
$900$		0			0
$901$	−50.2316	−	50.2316i	−1.67346	−	1.67346i
$902$		0			0
$903$			24.3063i			0.808861i
$904$		0			0
$905$		−	14.4398i		−	0.479996i
$906$		0			0
$907$	38.4478	+	38.4478i	1.27664	+	1.27664i	0.942537	+	0.334102i	$0.108433\pi$
$907$	38.4478	+	38.4478i	1.27664	+	1.27664i	0.334102	+	0.942537i	$0.391567\pi$
$908$		0			0
$909$	59.7484	−	59.7484i	1.98173	−	1.98173i
$910$		0			0
$911$	−28.5940			−0.947362			−0.473681	−	0.880697i	$-0.657075\pi$
$911$	−28.5940			−0.947362			−0.473681	+	0.880697i	$0.657075\pi$
$912$		0			0
$913$	21.7486			0.719773
$914$		0			0
$915$	8.06403	−	8.06403i	0.266589	−	0.266589i
$916$		0			0
$917$	1.10403	+	1.10403i	0.0364581	+	0.0364581i
$918$		0			0
$919$			14.6386i			0.482881i	0.970416	+	0.241441i	$0.0776199\pi$
$919$			14.6386i			0.482881i	−0.970416	+	0.241441i	$0.922380\pi$
$920$		0			0
$921$		−	76.7776i		−	2.52991i
$922$		0			0
$923$	7.06954	+	7.06954i	0.232697	+	0.232697i
$924$		0			0
$925$	−26.4373	+	26.4373i	−0.869253	+	0.869253i
$926$		0			0
$927$	98.5111			3.23553
$928$		0			0
$929$	48.8608			1.60307			0.801535	−	0.597948i	$-0.204017\pi$
$929$	48.8608			1.60307			0.801535	+	0.597948i	$0.204017\pi$
$930$		0			0
$931$	1.38948	−	1.38948i	0.0455385	−	0.0455385i
$932$		0			0
$933$	10.7344	+	10.7344i	0.351428	+	0.351428i
$934$		0			0
$935$			23.5347i			0.769667i
$936$		0			0
$937$		−	51.4306i		−	1.68016i	−0.542460	−	0.840081i	$-0.682507\pi$
$937$		−	51.4306i		−	1.68016i	0.542460	−	0.840081i	$-0.317493\pi$
$938$		0			0
$939$	−15.9725	−	15.9725i	−0.521243	−	0.521243i
$940$		0			0
$941$	−26.2233	+	26.2233i	−0.854856	+	0.854856i	−0.990727	−	0.135871i	$-0.956617\pi$
$941$	−26.2233	+	26.2233i	−0.854856	+	0.854856i	0.135871	+	0.990727i	$0.456617\pi$
$942$		0			0
$943$	−1.95289			−0.0635950
$944$		0			0
$945$	−6.68706			−0.217530
$946$		0			0
$947$	8.60278	−	8.60278i	0.279553	−	0.279553i	−0.553378	−	0.832930i	$-0.686661\pi$
$947$	8.60278	−	8.60278i	0.279553	−	0.279553i	0.832930	+	0.553378i	$0.186661\pi$
$948$		0			0
$949$	12.8087	+	12.8087i	0.415789	+	0.415789i
$950$		0			0
$951$			73.8526i			2.39484i
$952$		0			0
$953$		−	26.1027i		−	0.845549i	−0.906235	−	0.422775i	$-0.861056\pi$
$953$		−	26.1027i		−	0.845549i	0.906235	−	0.422775i	$-0.138944\pi$
$954$		0			0
$955$	−18.6704	−	18.6704i	−0.604160	−	0.604160i
$956$		0			0
$957$	−52.7988	+	52.7988i	−1.70674	+	1.70674i
$958$		0			0
$959$	0.184924			0.00597152
$960$		0			0
$961$	−3.57299			−0.115258
$962$		0			0
$963$	0.779727	−	0.779727i	0.0251264	−	0.0251264i
$964$		0			0
$965$	17.7253	+	17.7253i	0.570598	+	0.570598i
$966$		0			0
$967$			8.74115i			0.281097i	0.990074	+	0.140548i	$0.0448865\pi$
$967$			8.74115i			0.281097i	−0.990074	+	0.140548i	$0.955113\pi$
$968$		0			0
$969$			39.3160i			1.26301i
$970$		0			0
$971$	29.8601	+	29.8601i	0.958255	+	0.958255i	0.999163	−	0.0409077i	$-0.0130249\pi$
$971$	29.8601	+	29.8601i	0.958255	+	0.958255i	−0.0409077	+	0.999163i	$0.513025\pi$
$972$		0			0
$973$	−4.08707	+	4.08707i	−0.131026	+	0.131026i
$974$		0			0
$975$	−32.1478			−1.02955
$976$		0			0
$977$	−24.3299			−0.778383			−0.389191	−	0.921157i	$-0.627245\pi$
$977$	−24.3299			−0.778383			−0.389191	+	0.921157i	$0.627245\pi$
$978$		0			0
$979$	1.03771	−	1.03771i	0.0331653	−	0.0331653i
$980$		0			0
$981$	1.65052	+	1.65052i	0.0526971	+	0.0526971i
$982$		0			0
$983$		−	36.0892i		−	1.15107i	−0.817778	−	0.575534i	$-0.804794\pi$
$983$		−	36.0892i		−	1.15107i	0.817778	−	0.575534i	$-0.195206\pi$
$984$		0			0
$985$			9.77466i			0.311447i
$986$		0			0
$987$	9.48797	+	9.48797i	0.302005	+	0.302005i
$988$		0			0
$989$	12.2409	−	12.2409i	0.389239	−	0.389239i
$990$		0			0
$991$	−44.3921			−1.41016			−0.705080	−	0.709127i	$-0.749089\pi$
$991$	−44.3921			−1.41016			−0.705080	+	0.709127i	$0.749089\pi$
$992$		0			0
$993$	−2.86996			−0.0910754
$994$		0			0
$995$	−10.7030	+	10.7030i	−0.339307	+	0.339307i
$996$		0			0
$997$	1.44245	+	1.44245i	0.0456830	+	0.0456830i	0.729579	−	0.683896i	$-0.239716\pi$
$997$	1.44245	+	1.44245i	0.0456830	+	0.0456830i	−0.683896	+	0.729579i	$0.739716\pi$
$998$		0			0
$999$		−	62.7490i		−	1.98529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.f.449.2	yes	16
4.3	odd	2		1792.2.m.h.449.7	yes	16
8.3	odd	2		1792.2.m.e.449.2	✓	16
8.5	even	2		1792.2.m.g.449.7	yes	16
16.3	odd	4		1792.2.m.h.1345.7	yes	16
16.5	even	4		1792.2.m.g.1345.7	yes	16
16.11	odd	4		1792.2.m.e.1345.2	yes	16
16.13	even	4	inner	1792.2.m.f.1345.2	yes	16
32.3	odd	8		7168.2.a.bf.1.8		8
32.13	even	8		7168.2.a.ba.1.8		8
32.19	odd	8		7168.2.a.bb.1.1		8
32.29	even	8		7168.2.a.be.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.2	✓	16	8.3	odd	2
1792.2.m.e.1345.2	yes	16	16.11	odd	4
1792.2.m.f.449.2	yes	16	1.1	even	1	trivial
1792.2.m.f.1345.2	yes	16	16.13	even	4	inner
1792.2.m.g.449.7	yes	16	8.5	even	2
1792.2.m.g.1345.7	yes	16	16.5	even	4
1792.2.m.h.449.7	yes	16	4.3	odd	2
1792.2.m.h.1345.7	yes	16	16.3	odd	4
7168.2.a.ba.1.8		8	32.13	even	8
7168.2.a.bb.1.1		8	32.19	odd	8
7168.2.a.be.1.1		8	32.29	even	8
7168.2.a.bf.1.8		8	32.3	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04137 + 2.04137i) q^{3} +(-0.701647 - 0.701647i) q^{5} -1.00000i q^{7} -5.33435i q^{9} +O(q^{10})\)	\(q+(-2.04137 + 2.04137i) q^{3} +(-0.701647 - 0.701647i) q^{5} -1.00000i q^{7} -5.33435i q^{9} +(2.41989 + 2.41989i) q^{11} +(-1.96098 + 1.96098i) q^{13} +2.86464 q^{15} -6.93050 q^{17} +(-1.38948 + 1.38948i) q^{19} +(2.04137 + 2.04137i) q^{21} -2.05612i q^{23} -4.01538i q^{25} +(4.76526 + 4.76526i) q^{27} +(5.34414 - 5.34414i) q^{29} +5.23708 q^{31} -9.87975 q^{33} +(-0.701647 + 0.701647i) q^{35} +(-6.58401 - 6.58401i) q^{37} -8.00617i q^{39} -0.949797i q^{41} +(5.95343 + 5.95343i) q^{43} +(-3.74283 + 3.74283i) q^{45} +4.64785 q^{47} -1.00000 q^{49} +(14.1477 - 14.1477i) q^{51} +(7.24791 + 7.24791i) q^{53} -3.39582i q^{55} -5.67289i q^{57} +(-8.58048 - 8.58048i) q^{59} +(2.81502 - 2.81502i) q^{61} -5.33435 q^{63} +2.75184 q^{65} +(-9.07198 + 9.07198i) q^{67} +(4.19729 + 4.19729i) q^{69} -3.60510i q^{71} -6.53179i q^{73} +(8.19686 + 8.19686i) q^{75} +(2.41989 - 2.41989i) q^{77} +13.7819 q^{79} -3.45223 q^{81} +(4.49372 - 4.49372i) q^{83} +(4.86277 + 4.86277i) q^{85} +21.8187i q^{87} -0.428825i q^{89} +(1.96098 + 1.96098i) q^{91} +(-10.6908 + 10.6908i) q^{93} +1.94986 q^{95} +14.6339 q^{97} +(12.9085 - 12.9085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 4 q^{5}+O(q^{10}) \) 16 * q - 4 * q^3 + 4 * q^5	\( 16 q - 4 q^{3} + 4 q^{5} + 8 q^{11} - 12 q^{13} - 8 q^{17} - 4 q^{19} + 4 q^{21} + 56 q^{27} + 8 q^{31} + 16 q^{33} + 4 q^{35} + 8 q^{37} + 24 q^{43} + 36 q^{45} + 40 q^{47} - 16 q^{49} - 24 q^{51} + 32 q^{53} + 4 q^{59} + 20 q^{61} - 24 q^{63} + 72 q^{65} - 32 q^{67} - 56 q^{69} + 28 q^{75} + 8 q^{77} - 40 q^{81} - 36 q^{83} + 12 q^{91} - 8 q^{93} + 80 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 + 4 * q^5 + 8 * q^11 - 12 * q^13 - 8 * q^17 - 4 * q^19 + 4 * q^21 + 56 * q^27 + 8 * q^31 + 16 * q^33 + 4 * q^35 + 8 * q^37 + 24 * q^43 + 36 * q^45 + 40 * q^47 - 16 * q^49 - 24 * q^51 + 32 * q^53 + 4 * q^59 + 20 * q^61 - 24 * q^63 + 72 * q^65 - 32 * q^67 - 56 * q^69 + 28 * q^75 + 8 * q^77 - 40 * q^81 - 36 * q^83 + 12 * q^91 - 8 * q^93 + 80 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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